Gas turbine combustor and gas turbine

ABSTRACT

Provided are a gas turbine combustor and a gas turbine, with which the amount of NOx exhaust emissions from a diffuse combustion-type duct burner can be reduced. A duct burner is provided with cylindrical fuel injection nozzles and air holes. The fuel injection nozzles are supported by an outside casing along eight axial centers included within a plane orthogonal to a center axis and arranged at equidistant intervals (45-degree intervals) in the circumferential direction. Sets of eight fuel injection nozzles are respectively constituted as single fuel injection nozzle rows, four fuel injection nozzle rows being arrayed at prescribed spacing along a direction of a center axis. The angular positions of the fuel injection nozzles are arrayed so as to be shifted by a half-pitch angle in opposing rows.

TECHNICAL FIELD

The present invention relates to a combustor for use with a gas turbine engine and a gas turbine engine.

BACKGROUND

With regard to gas turbine engines, a strict environmental standard has been established for an amount of nitrogen oxide (hereinafter referred to as “NOx”) contained in a gas exhausted from the gas turbine engine.

The applicant of this application has proposed a combustor for use with a gas turbine engine, which comprises a plurality of premixed combustion type main burners arranged on an upstream side (i.e., first combustion region) of a combustion chamber and a plurality of diffusion combustion type reheating burners each positioned on a downstream side (i.e., second combustion region) of the combustion chamber to oppose an associated dilution air supply opening, for introducing a combustion air into the combustion chamber (see, for example, Patent Document 1).

PRIOR ART DOCUMENT Patent Document

Patent Document 1: JP 8-210641 A

SUMMARY OF THE INVENTION Technical Problem

Advantageously, the gas turbine combustor described in Patent Document 1 has a reduced risk of backfire due to the employment of the diffusion combustion type reheating burners. However, an increase of the fuel flow rate may increase the fuel concentration in the combustion region for the reheating burners and the resultant combustion temperature, which disadvantageously increases the amount of NOx emission.

It is therefore an object of the present invention to reduce the amount of NOx emission from the diffusion combustion type reheating burner in the gas turbine combustor and the gas turbine with the structure described above.

A combustor for use with a gas turbine engine of the present invention is a gas turbine combustor for mixing and combusting a fuel with a compressed air introduced from a compressor and supplying a generated combustion exhaust gas to a gas turbine, comprising a combustion cylinder forming a combustion chamber therein; a premixed combustion type main burner disposed on an upstream side of the combustion cylinder; and a plurality of diffusion combustion type reheating burners disposed on a downstream side of the main burner to extend through a peripheral wall of the combustion cylinder for injecting a fuel from the peripheral wall into the combustion chamber, the plurality of reheating burners being aligned in a circumferential direction and an axial direction of the combustion cylinder.

According to this arrangement, since the main burner is of the premixed combustion type, an amount of NOx in the high-temperature combustion gas generated in a primary combustion region on the upstream side of the combustion chamber is reduced. Since the plurality of reheating burners are aligned in the circumferential direction and the axial direction of the combustion cylinder and the reheating fuel is distributed and supplied from the reheating burners to the combustion chamber, a fuel flow rate per reheating burner is reduced as compared to when the plurality of reheating burners is arranged in alignment with the circumferential direction. Therefore, the fuel concentration becomes thinner in the combustion region of the reheating burners, so that the combustion temperature of the reheating burners is generally kept lower, and the amount of NOx in the combustion gas can consequently be reduced.

The plurality of reheating burners in neighborhood arrays may be disposed in a staggered fashion in the circumferential direction.

According to this configuration, by arranging the reheating burners in staggered fashion in the circumferential direction, the combustion of the reheating burners arranged on the downstream side is hardly affected by the combustion of the reheating burners arranged on the upstream side, and the combustion of the reheating burners on the downstream side can be stabilized.

The combustor may comprise a fuel header configured to distribute the fuel to the plurality of reheating burners.

According to this configuration, the fuel can evenly be distributed with a simple configuration to the plurality of reheating burners.

The combustor may comprise a first fuel header configured to distribute a first fuel mainly composed of methane to a predetermined number of reheating burners among the plurality of reheating burners, and a second fuel header distributing a second fuel composed of a hydrogen gas or a hydrogen-containing gas to the remaining predetermined number of reheating burners.

According to this configuration, the fuel can be distributed with a simple structure to the plurality of reheating burners.

A gas turbine engine of the present invention includes any one of the combustors described above. According to this configuration, a gas turbine engine equipped with a combustor capable of suppressing an amount of NOx emission can be provided.

According to the present invention, the combustor and the gas turbine engine are capable of reducing the amount of NOx emission.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram schematically showing a general construction of a gas turbine according to an embodiment of the present invention.

FIG. 2 is a longitudinal sectional view of a combustor according to an embodiment of the present invention.

FIG. 3A is an axial cross-sectional view of the combustor taken along lines A-A in FIG. 2.

FIG. 3B is an axial cross-sectional taken along lines B-B in FIG. 2.

FIG. 3C is an axial cross-sectional view of the combustor taken along lines C-D in FIG. 2.

FIG. 3D is an axial cross-sectional taken along lines D-D in FIG. 2.

FIG. 4 is a cross-sectional view of a modification of a reheating burner (fuel injection nozzle).

DESCRIPTION OF THE EMBODIMENTS

With reference to the accompanying drawings, several embodiments of a combustor of use with a gas turbine engine and a gas turbine according to present invention will be described. The following description merely shows embodiments of the invention and is not intended to limit the present invention, an application thereof, or a use thereof.

FIG. 1 is a schematic diagram of a general construction and functions of the gas turbine engine. The gas turbine engine 1 has a compressor 2 taking in atmospheric air to generate compressed air 200. The compressed air 200 is combusted together with fuel in the combustor 3 to generate high-temperature high-pressure combustion gas (hereinafter referred to as “combustion exhaust gas”) 300. The combustion exhaust gas 300 is supplied to a turbine 4 where it is used for rotating a rotor 5. The rotation of the rotor 5 is transmitted to the compressor 2 where it is used for generating the compressed air (hereinafter referred to as “combustion air”) 200. The rotation of the rotor 5 is transmitted to, for example, a generator 6 where it is used for electric generation.

FIG. 2 shows the combustor 3. In this embodiment, the combustor 3 is a reverse-flow can-type combustor in which the compressed air 200 supplied from the compressor (see FIG. 1) flows in one direction (downward direction in FIG. 1) and the combustion exhaust gas 300 flows in the opposite direction (upward direction in FIG. 1). The combustor may be an annular type combustor in which a plurality of fuel injection valves are provided at intervals in a peripheral direction of the combustor.

The combustor 3 includes a combustion cylinder 34 and a casing 35, both coaxially arranged on a central axis 302. A burner unit 30 is mounted on the top of the combustion cylinder 34. The combustion cylinder 34 defines thereinside a combustion chamber 33 for combusting fuel injected therein from the burner unit 30. The combustion cylinder 34 is surrounded by a cylindrical casing 35 to form between the combustion cylinder 34 and the casing 35 an annular combustion air flow path 37 through which the combustion air 200 supplied from the compressor flows. The casing 35 and the combustion cylinder 34 support a plurality of reheating burners 36 on a downstream side of the burner unit 30.

In this embodiment, the burner unit 30 includes a premixing type main burner 31 disposed along the central axis 302 for injecting a premixed gas generated by mixing a fuel and the combustion air 200 into the combustion chamber 33 and a diffusion combustion type pilot burner 32 for directly injecting a fuel into the combustion chamber 33. The main burner 31 is coaxially disposed around the pilot burner 32. The main burner 31 and the pilot burner 32 communicate with a first fuel supply source 305 through pipes 304.

In this embodiment, the main burner 31 has an outer cylinder 310 and an inner cylinder 312 arranged coaxially along the central axis 302. As shown, the inner cylinder 312 also serves as a combustion air injection cylinder 322 b of the pilot burner 32 described later. An annular space between the outer cylinder 310 and the inner cylinder 312 is used as a premixing flow path 314 for mixing the fuel and the combustion air. The pilot burner 32 includes a fuel injection cylinder 322 a extending along the central axis 302 and the combustion air injection cylinder 322 b coaxially mounted on the fuel injection cylinder 322 a, and a fuel injection path (not shown) formed in the fuel injection cylinder 322 a is connected to the first fuel supply source 305 through the pipe 304 b including a flow regulating valve, so that by opening the flow regulating valve at the start-up operation, a natural gas supplied from the first fuel supply source 305 is injected into the combustion chamber 33. An annular air flow path 324, which is formed between the fuel injection cylinder 322 a and the combustion air injection cylinder 322 b, is connected at one end thereof to the combustion air flow path 37 and at the other end thereof to the combustion chamber 33, so that the combustion air 200 supplied from the compressor is injected into the combustion chamber 33.

The premixing flow path 314 has one end opened to the combustion chamber 33 and the other end oriented radially outwardly and opened to the combustion air flow path 37 through a plurality of air intake ports 315. A plurality of primary fuel nozzles 316 ejecting a first fuel is arranged radially outside the air intake ports 315. Although not shown, preferably, the air intake ports 315 and the associated primary fuel nozzles 316 are arranged at regular intervals in the circumferential direction around the center axis 302.

The primary fuel nozzles 316, each having a plurality of fuel injection holes (not shown) formed at a position facing the air intake port 315 so as to eject the first fuel toward the air intake port 315, are connected to the first fuel supply source 305 through the pipes 304 a with a flow regulating valve. This allows that, when the flow regulating valve is opened in the normal operation, the fuel from the first fuel supply source 305 is supplied from the air intake ports 315 to the premixing flow path 314 where the fuel is premixed with the combustion air 200 supplied from the combustion air flow path 37 and then is injected into the combustion chamber 33. In this embodiment, a plurality of swirl vane members or swirlers 317 are provided in the air intake ports 315 to impart a swirling force to the combustion air 200 flowing into the premixing flow path 314 so as to promote the premixing with the first fuel.

The reheating burners 36, which are diffusion combustion type burners, include cylindrical fuel injection nozzles 38 and air holes 340. As shown in FIG. 3, the fuel injection nozzles 38 are attached to both the casing 35 and the combustion cylinder 34 along eight axial centers 360 included on respective planes orthogonal to the central axis 302 and arranged at regular angles of 45 degrees in the circumferential direction. In this embodiment, eight fuel injection nozzles 38 a-1 to 38 a-8, 38 b-1 to 38 b-8, 38 c-1 to 38 c-8, 38 d-1 to 38 d-8 constitute respective fuel injection nozzle arrays, and four fuel injection nozzle arrays 38 a, 38 b, 38 c, 38 d are arranged at predetermined intervals along the direction of the central axis 302 (see FIG. 2).

As shown in FIGS. 2 and 3, in this embodiment, upstream end portions of the fuel injection nozzles 38 a-1 to 38 a-8, 38 c-1 to 38 c-8 constituting the fuel injection nozzle arrays 38 a, 38 c are connected to first fuel headers 39 a, 39 c distributing the first fuel to the fuel injection nozzles 38 a-1 to 38 a-8, 38 c-1 to 38 c-8. The first fuel headers 39 a, 39 c are connected to the first fuel supply source 305 through a pipe 306 with a flow regulating valve.

Also, upstream end portions of the fuel injection nozzles 38 b-1 to 38 b-8, 38 d-1 to 38 d-8 constituting the fuel injection nozzle arrays 38 b, 38 d are connected to second fuel headers 39 b, 39 d distributing a second fuel to the fuel injection nozzles 38 b-1 to 38 b-8, 38 d-1 to 38 d-8. The second fuel headers 39 b, 39 d are connected to a second fuel supply source 307 through a pipe 308 including a flow regulating valve such that the first fuel and the second fuel can be injected into the combustion chamber 33 by opening the flow regulating valve in a high-load operation. The first fuel is a gas containing 60 vol % or more hydrocarbons with hydrogen gas equal to or less than 10 vol %, or a liquid containing 60 vol % or more hydrocarbons. The second fuel is a gas containing 50 vol % or more hydrogen. In this embodiment, a natural gas may be an example of the first fuel and a hydrogen gas may be an example of the second fuel.

The first and second fuel headers 39 a, 39 c, 39 b, and 39 d extend annularly around the outer casing 35. The combustion cylinder 34 has air holes 340 associated with the fuel injection nozzles 38 a-1 to 38 a-8, 38 b-1 to 38 b-8, 38 c-1 to 38 c-8, and 38 d-1 to 38 d-8 so that a part of the compressed air 200 is introduced as combustion air into the combustion chamber 33 around the fuel injection nozzles 38 a-1 to 38 a-8, 38 b-1 to 38 b-8, 38 c-1 to 38 c-8, and 38 d-1 to 3 d-8 (see FIGS. 2 and 3).

Features of the combustor 3 of this embodiment will hereinafter be described. FIGS. 3A to 3D show cross sections taken along lines A-A, B-B, C-C, and D-D and viewed in the direction of arrows of FIG. 2. As shown in FIGS. 3A and 3C, the angular positions of the eight fuel injection nozzles 38 a-1 to 38 a-8 constituting the fuel injection nozzle array 38 a are coincident with the angular positions of the eight fuel injection nozzles 38 c-1 to 38 c-8 constituting the fuel injection nozzle arrays 38 c.

As shown in FIG. 3B, the angular positions of the eight fuel injection nozzles 38 b-1 to 38 b-8 constituting the fuel injection nozzle array 38 b are shifted by a half-pitch angle (22.5 degrees) relative to the angular positions of the eight fuel injection nozzles 38 a-1 to 38 a-8, 38 c-1 to 38 c-8 of each of the facing fuel injection nozzle arrays 38 a, 38 c.

As shown in FIG. 3D, the angular positions of the eight fuel injection nozzles 38 d-1 to 38 d-8 constituting the fuel injection nozzle array 38 d are shifted by the half-pitch angle (22.5 degrees) relative to the angular positions of the eight fuel injection nozzles 38 c-1 to 38 c-8 of the facing fuel injection nozzle array 38 c. Therefore, the fuel injection nozzles 38 a-1 to 38 a-8, 38 b-1 to 38 b-8, 38 c-1 to 38 c-8, 38 d-1 to 38 d-8 arranged in the neighborhood arrays are in a staggered arrangement.

An operation of the combustor 3 so constructed will hereinafter be described with reference to FIG. 2. As shown in the drawing, when a gas turbine (not shown) is started, the flow regulating valve is opened so that the first fuel (natural gas) supplied from the first fuel supply source 305 through the piping 304 b to the pilot burner 32 is injected into the combustion chamber 33. Subsequently, the first fuel is diffusively mixed in the combustion chamber 33 with the combustion air 200 injected from the annular air flow path 324 into the combustion chamber 33. The mixture is then ignited by an ignition source not shown to form a pilot flame from diffusion combustion.

When the gas turbine changes into a normal operation, the first fuel from the first fuel supply source 305 through the pipes 304 to the primary fuel nozzles 316 and the combustion air 200 flowing in from the air intake ports 315 are mixed with each other in the premixing flow path 314 to generate a premixed gas. Subsequently, the premixed gas is injected from the premixing flow path 314 and then ignited by the pilot flame in the combustion chamber 33 and combusted in a primary combustion region S1 on the proximal side of the combustion chamber 33. As described above, the lean premixed gas is combusted, which results in that a combustion flame temperature in the combustion chamber 33 is reduced and, therefore, an amount of NOx in the combustion exhaust gas of the main burner 31 is minimized.

When high-load combustion is requested to raise the output of the gas turbine, the reheating burners 36 are operated. Specifically, the first fuel is supplied to the first fuel headers 39 a and 39 c. The supplied first fuel is evenly distributed to the eight fuel injection nozzles 38 a-1 to 38 a-8 constituting the fuel injection nozzle array 38 a and the eight fuel injection nozzles 38 c-1 to 38 c-8 constituting the fuel injection nozzle array 38 c and then injected into the flow of the combustion exhaust gas 300 from outside thereof.

Similarly, the second fuel (hydrogen gas) supplied to the second fuel headers 39 b, 39 d, is evenly distributed to the eight fuel injection nozzles 38 b-1 to 38 b-8 constituting the fuel injection nozzle array 38 b and the eight fuel injection nozzles 38 d-1 to 38 d-8 constituting the fuel injection nozzle array 38 d and then injected into the flow of the combustion exhaust gas 300 from outside thereof. The amount of and the ratio of the first fuel (natural gas) and the second fuel (hydrogen gas) supplied are appropriately determined in accordance with combustion conditions.

As described above, the arrangement of the first fuel headers 39 a, 39 c and the second fuel headers 39 b, 39 d allows the intended fuel to be distributed evenly to the eight fuel injection nozzles 38 a-1 to 38 a-8, 38 b-1 to 38 b-8, 38 c-1 to 38 c-8, 38 d-1 to 38 d-8 with a simple structure.

The first fuel injected from the fuel injection nozzles 38 a-1 to 38 a-8, 38 c-1 to 38 c-8 and the second fuel injected from the fuel injection nozzles 38 b-1 to 38 b-8, 38 d-1 to 38 d-8 are diffusively mixed with a portion of the combustion air 200 flowing into the combustion chamber 33 through the air holes 340 from the circumferences of the fuel injection nozzles 38 a-1 to 38 a-8, 38 b-1 to 38 b-8, 38 c-1 to 38 c-8, 38 d-1 to 38 d-8. Since the reheating fuels (the natural gas and the hydrogen gas) are distributed and supplied from the fuel injection nozzles 38 a-1 to 38 a-8, 38 b-1 to 38 b-8, 38 c-1 to 38 c-8, 38 d-1 to 38 d-8 into the combustion chamber 33, a fuel flow rate of each of the reheating burners 36 is reduced. Therefore, the fuel concentration becomes thinner in the combustion region of the reheating burners 36 as compared to when a plurality of the reheating burners 36 is arranged only in the circumferential direction, so that the overall combustion temperature is kept lower and, as a result, the amount of NOx in the combustion gas 300 which may be dependent on the combustion temperature is minimized.

As described above, according to the embodiment of the present invention the fuel injection nozzles 38 a-1 to 38 a-8, 38 b-1 to 38 b-8, 38 c-1 to 38 c-8, 38 d-1 to 38 d-8 in the neighborhood arrays of the combustor 3 are arranged in the staggered fashion with respect to the circumferential direction. With this arrangement, the combustion of the reheating burners arranged on the downstream side is hardly affected by the combustion of the reheating burners arranged on the upstream side, which stabilizes the combustion of the reheating burners on the downstream side. The angular positions of the eight fuel injection nozzles 38 a-1 to 38 a-8, 38 b-1 to 38 b-8, 38 c-1 to 38 c-8, 38 d-1 to 38 d-8, constituting each of the four fuel injection nozzles arrays 38 a, 38 b, 38 c, and 38 d may be the same.

The combustion exhaust gas 300 increased by combustion of the first and second fuels introduced from the reheating burners 36 is fed into the gas turbine and used for output adjustment of the gas turbine.

The embodiment described above may be modified in various ways. For example, in the above embodiment, the hydrogen gas is injected as the second fuel from the fuel injection nozzles 38 b-1 to 38 b-8, 38 d-1 to 38 d-8. Since the hydrogen gas has the mass considerably smaller than the mass of air (a mixture of oxygen and nitrogen), the hydrogen gas simply applied to the flow of combustion exhaust gas 300 from the side thereof may not reach a mainstream (central portion) of the flow of the combustion exhaust gas 300. Therefore, for example, as shown in FIGS. 4A and 4B, a throttle part 40 may be formed at an opening in a downstream end portion of each of the fuel injection nozzles 38 b-1 to 38 b-8 (38 d-1 to 38 d-8) to increase a kinetic energy at the time of ejection of the hydrogen gas. With the arrangement, the hydrogen gas can purposely be fed into the mainstream (central portion) of the flow of the combustion product gas. As a result, a combustion flame having uniform concentration distribution as a whole can be formed in a secondary combustion region S2.

Although the first fuel is supplied to the fuel injection nozzle arrays 38 a, 38 c and the second fuel is supplied to the fuel injection nozzle arrays 38 b, 38 d in the configuration exemplified in the embodiment described above, the present invention is not limited thereto. The fuel headers can be produced in a proper structure to employ a configuration such that, for example, the first fuel is injected from the fuel injection nozzles 38 a-1, 38 a-3, 38 a-5, 38 a-7 out of the fuel injection nozzles 38 a-1 to 38 a-8 while the second fuel is injected from the remaining fuel injection nozzles 38 a-2, 38 a-4, 38 a-6, 38 a-8 (the same applies to the fuel injection nozzles 38 b-1 to 38 b-8, 38 c-1 to 38 c-8, 38 d-1 to 38 d-8 constituting the fuel injection nozzle arrays 38 b, 38 c, 38 d).

Although the four fuel injection nozzle arrays 38 a, 38 b, 38 c, 38 d are arranged at predetermined intervals along the direction of the center axis 302 in the exemplary embodiment described above, the number of the fuel injection nozzle arrays may be at least two or more, and the number can be changed as needed. Although the fuel injection nozzles 38 are supported at eight positions on the casing 35 on the outside at regular intervals (intervals of 45 degrees) in the exemplary embodiment described above, the number of the fuel injection nozzles 38 may be at least two or more, and the number can be changed as needed. The pitch angle shifting the angular position of the fuel injection nozzles in the facing fuel injection nozzle arrays may also be changed in accordance with the number of the fuel injection nozzles 38.

Although the first fuel is supplied to the first fuel headers 39 a, 39 c and the second fuel is supplied to the second fuel headers 39 b, 39 d in the exemplary embodiment described above, the first fuel or the second fuel may be supplied to all of the first fuel headers 39 a, 39 c and the second fuel headers 39 b, 39 d in accordance with the invention.

PARTS LIST

-   1 gas turbine -   2 compressor -   3 combustor -   4 turbine -   5 rotor -   6 generator -   31 main burner -   32 pilot burner -   33 combustion chamber -   34 combustion cylinder -   36 reheating burner -   37 combustion air flow path (air flow path) -   38 fuel injection nozzle -   38 a to 38 d fuel injection nozzle array -   39 a, 39 c first fuel header -   39 c, 39 d second fuel header -   40 throttle part -   200 compressed air (combustion air) -   300 combustion exhaust gas -   302 central axis -   360 axial center 

1. A combustor for use with a gas turbine engine, for mixing and combusting a fuel with a compressed air introduced from a compressor and supplying a generated combustion exhaust gas to a gas turbine, comprising: a combustion cylinder forming a combustion chamber therein; a premixed combustion type main burner disposed on an upstream side of the combustion cylinder; and a plurality of diffusion combustion type reheating burners disposed on a downstream side of the main burner to extend through a peripheral wall of the combustion cylinder for injecting a fuel from the peripheral wall into the combustion chamber, the plurality of reheating burners being aligned in a circumferential direction and an axial direction of the combustion cylinder.
 2. The combustor according to claim 1, wherein the plurality of reheating burners in neighborhood arrays are disposed in a staggered fashion in the circumferential direction.
 3. The combustor according to claim 1, comprising a fuel header configured to distribute the fuel to the plurality of reheating burners.
 4. The combustor according to claim 1, comprising a first fuel header configured to distribute a first fuel mainly composed of methane to a predetermined number of reheating burners among the plurality of reheating burners, and a second fuel header configured to distribute a second fuel composed of a hydrogen gas or a hydrogen-containing gas to the remaining reheating burners.
 5. A gas turbine engine comprising the combustor according to claim
 1. 6. A gas turbine engine comprising the combustor according to claim
 2. 7. A gas turbine engine comprising the combustor according to claim
 3. 8. A gas turbine engine comprising the combustor according to claim
 4. 1. A combustor for use with a gas turbine engine, for mixing and combusting a fuel with a compressed air introduced from a compressor and supplying a generated combustion exhaust gas to a gas turbine, comprising: a combustion cylinder forming a combustion chamber therein; a premixed combustion type main burner disposed on an upstream side of the combustion cylinder; and a plurality of diffusion combustion type reheating burners disposed on a downstream side of the main burner to extend through a peripheral wall of the combustion cylinder for injecting a fuel from the peripheral wall into the combustion chamber, the plurality of reheating burners being aligned in a circumferential direction and an axial direction of the combustion cylinder.
 2. The combustor according to claim 1, wherein the plurality of reheating burners in neighborhood arrays are disposed in a staggered fashion in the circumferential direction.
 3. The combustor according to claim 1 or 2, comprising a fuel header configured to distribute the fuel to the plurality of reheating burners.
 4. The combustor according to any one of claims 1 to 3, comprising a first fuel header configured to distribute a first fuel mainly composed of methane to a predetermined number of reheating burners among the plurality of reheating burners, and a second fuel header configured to distribute a second fuel composed of a hydrogen gas or a hydrogen-containing gas to the remaining reheating burners.
 5. A gas turbine engine comprising the combustor according to any one of claims 1 to
 4. 